Optimal modification of tooth flank form error considering measurement and compensation of cutter geometric errors for spiral bevel and hypoid gears

Abstract

In design and manufacturing for the spiral bevel and hypoid gear, the cutter geometric errors (CGEs) is one of main factors affecting tooth flan flank form error. To get an accurate and effective modification of tooth flank form error, a novel optimization and operation approach is proposed by correlating with measurement and compensation of CGEs. Firstly, an accurate modification model with optimal machine settings is developed as a nonlinear least square problem. Where, a small number of machine settings are selected as unknown optimal design variable by sensitivity analysis method. Then, CGEs are defined and their influences on the tooth flank form error are investigated for synthesis and analysis of the accurate higher-order modification. Finally, the optimal modification with small number of machine settings is performed based on measurement of the Doppler Laser interferometer MCV2002 following ISO 230-2(1997) standard and numerical control (NC) compensation of CGEs. In additional to the optimal design parameters is set to improve computational efficiency, the Levenberg–Marquardat (L–M) algorithm with trust-region strategy is applied to solve for the new machine settings with modification variations. A numerical application to a real case is designed to identify the validity of the proposed methodology.